Pt1420 Unit 6 Research Paper

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Math Assignment | May 11 2012 | | 1) Is the relationship between hours of daylight and day of year periodic in nature? Justify your answer. Yes, the relationship between hours of daylight and day of year periodic is in nature. It is because there are 365.25 days in one year and four years for one period which means there are going to have four same data in the whole period. And there is going to have the same maximum and minimum for four times. Therefore, this relationship is a periodic. 2) Using the graph determine the function‘s (a) Amplitude= (Max. - Min. )/2 = (15.45- 8.95) /2 = 3.25 (b) Period= 360 (c) Phase Shift= vertical reflection, vertical stretched by factor of 3 (d) Translation= 12.2 units upward (3)…show more content…
Show all work. Compare and discuss your answer. In my sine function, f(x)= 3.25sin(1/2x)+8.96 f(80)= 3.25sin(1/2x80)+8.96 = 11.05 In my cosine function, f(x)= -3.25cosx+ 12.2 f(80)= -3.25cos80+ 12.2 = 11.64 It is quite obvious that my cosine function is more explicit than my sine function. For instance, day 80 is between day 75 and day 90 which means it should between 11.16 and 11.86. And my sine function doesn’t even reach day 75’s level. However, my cosine function is more explicit. It shows us that there are 11.64 hours in day 80 which is right between 11.16 and 11.86. I think the cosine function is a reliable function in this case. (9) In my cosine function, -3.25cosx+ 12.2= 14 x= 123.6 By the data, there are about 241- 121= 120 days that are having 14 hours or above hours of daylight. Therefore, my equation- cosine should be correct because the different between my cosine function and the data is not more 3 hours. However, my sine function cannot be counted because there is an error for

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